$D _ { t } [ \mathbf { r } ( t ) \times \mathbf { u } ( t ) ] \text { given the following }$

question 29

Multiple Choice

$D _ { t } [ \mathbf { r } ( t ) \times \mathbf { u } ( t ) ] \text { given the following }$ Use the properties of the derivative to find vector-valued functions. $$\begin{array} { l } \mathbf { r } ( t ) = 2 t \mathbf { i } - 3 t ^ { 3 } \mathbf { j } + 3 t ^ { 2 } \mathbf { k } \\\mathbf { u } ( t ) = 3 \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 4 t ^ { 3 } \mathbf { k }\end{array}$$

• A) \(\left( - 60 t ^ { 3 } - 72 t ^ { 5 } \right) \mathbf { i } + \left( 18 t ^ { 2 } - 32 t ^ { 3 } \right) \mathbf { j } + 57 t ^ { 2 } \mathbf { k }\)
• B) \(\left( - 60 t ^ { 3 } - 72 t ^ { 5 } \right) \mathbf { i } + \left( 32 t + 18 t ^ { 3 } \right) \mathbf { j } + 57 t ^ { 2 } \mathbf { k }\)
• C) \(\left( - 60 t ^ { 3 } - 72 t ^ { 5 } \right) \mathbf { i } + \left( 18 t - 32 t ^ { 3 } \right) \mathbf { j } - 3 t ^ { 2 } \mathbf { k }\)
• D) \(\left( - 60 t ^ { 3 } - 72 t ^ { 5 } \right) \mathbf { i } + \left( 18 t - 32 t ^ { 3 } \right) \mathbf { j } + 57 t ^ { 2 } \mathbf { k }\)
• E) \(\left( - 60 t ^ { 3 } - 72 t ^ { 5 } \right) \mathbf { i } + \left( 18 t + 32 t ^ { 3 } \right) \mathbf { j } + 57 t ^ { 3 } \mathbf { k }\)

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